Abstract
As was pointed out in the introduction, measures of dispersion, such as standard errors, have never been calculated for the estimated coefficients in a cross-sectionally based interindustry model. However, empirical inputoutput models have been subjected to other types of experiments in order to determine their effectiveness in representing actual economic systems. The purpose of this chapter is to review some of the more widely used experiments with a view toward showing why they have been inconclusive. Specifically, the discussion to follow will provide the groundwork for a more powerful and more comprehensive test of the input-output approach. The material presented in this chapter will be neither comprehensive in its coverage nor detailed in its evaluation. Rather, it is meant to provide a set of ideas which will be expanded in subsequent chapters.
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Notes
For more detailed treatments of the structure of input-output systems, see Otto Eckstein, ‘The Input-Output System — Its Nature and Use,’ Economic Activity Analysis, ed. Oskar Morganstern, New York, John Wiley and Sons, 1954, pp. 43–78; Robert Dorfman, Paul A. Samuelson and Robert M. Solow, Linear Programming and Economic Analysis, New York, McGraw-Hill, 1958; and William H. Miernyk, The Elements of Input-Output Analysis, New York, Random House, 1965.
Hollis B. Chenery and Paul G. Clark, Interindustry Economics, New York, John Wiley and Sons, 1959, pp. 33–42.
On this point, see Paul A. Samuelson, ‘Abstract of a Theorem Concerning Substitution in Open Leontief Systems,’ Activity Analysis of Production and Allocation, ed. Tjalling Koopmans, New York, John Wiley and Sons, 1951; and Sanjit Bose, ‘A New Proof of the Non-Substitution Theorem,’ International Economic Review, XIII, February, 1972.
Robert Dorfman, Paul A. Samuelson, and Robert M. Solow, Linear Programming and Economic Analysis, New York, McGraw-Hill, 1958, p. 231. Also note that if all inputs are perfectly divisible and if there is no waste, the minimum of the elements (a,b,…, z) will equal the maximum.
The issue of measurement errors in an input-output setting has been previously discussed by two authors. C. B. Tilanus, Input Output Experiments: The Netherlands, 1948–1961, Rotterdam, Rotterdam University Press, 1966. Michael Bacharach, Biproportional Matrices and Input-Output Change, Cambridge, Cambridge University Press, 1970.
See also P. N. Rasmussen, Studies in Intersectoral Relations, Amsterdam, North-Holland, 1956, pp. 45–47; and Leonid Hurwicz, ‘Input-Output Analysis and Economic Structure,’ American Economic Review, XLV, September, 1955, 631.
Lawrence Klein, A Textbook of Econometrics, Englewood Cliffs, N.J., Prentice-Hall, 1974, pp. 341–42.
For a recent review of this literature, see Bacharach, Biproportional Matrices and Input Output Change, pp. 10–16.
Often, these studies will appear to be somewhat dated. However, the more recent efforts, which will be indicated in the bibliography, typically obtain the same or similar results. In addition, they are usually less comprehensive.
Burgess Cameron, ‘The Production Function in Leontief Models,’ The Review of Economic Studies, XX(1), 1952–1953.
Chenery and Clark, Interindustry Economics, p. 164.
Per Sevaldson, ‘Changes in Input-Output Coefficients,’ Structural Interdependence and Economic Development, ed. Tibor Barna, New York, St. Martin’s Press, 1963. Sevaldson also examined the wood products sector. His results are not reproduced here as they are much the same as for the cork products sector.
Ibid., p. 315.
C. B. Tilanus, Input-Output Experiments: The Netherlands 1948–1961, Rotterdam, Rotterdam University Press, 1966, pp. 36–51.
C. B. Tilanus and Henri Theil, ‘The Information Approach to the Evaluation of Input Output Forecasts,’ Econometrica, XXXII, October, 1965.
For example, see Ann P. Carter, Structural Change in the American Economy, Cambridge, Mass., Harvard University Press, 1970.
Rasmussen, Studies in Intersectoral Relations, p. 129.
An exception is Kenneth J. Arrow and Marvin M. Hoffenberg, A Time Series Analysis of Interindustry Demands, Amsterdam, North-Holland, 1959. This study will be reviewed in the final section.
Harold J. Barnett, ‘Specific Industry Output Projections,’ Long Range Economic Projection, ed. National Bureau of Economic Research, Princeton, Princeton University Press, 1954.
Ibid., p. 202.
A. A. Adams and I. G. Stewart, ‘Input-Output Analysis: An Application,’ The Economic Journal, LXVI, September, 1956.
Ibid., 451.
Other methods for updating matrices of technical coefficients have been proposed in Tilanus, Input-Output Experiments: The Netherlands, 1948–1961 and in Bacharach, Biproportional Matrices and Input-Output Change. The interested reader may consult these books for a more thorough treatment of this topic.
Department of Applied Economics, University of Cambridge, ‘Input-Output Relation-ships 1954–1966,’ A Programme for Growth, ed. Richard Stone, London, Chapman and Hall, 1963, p. 28.
Ibid.
Bacharach, Biproportional Matrices, pp. 27–30.
Arrow gand Hoffenberg, A Time Series of Interindustry Demands.
Richard E. Quandt, ‘On the Solution of Probabilistic Leontief Systems,’ Naval Research Logistics Quarterly, VI, December, 1959. For another, and more recent, study in this vein, see Paul H. Tomlin, ‘An Error Model for Projected Gross Outputs Using an Input Output Table,’ Bureau of Census Research Memorandum No. 212, 1973 and Paul H. Tomlin, ‘Input-Output Error Analysis-Present Status,’ Bureau of Census Research Memorandum, No. 317, 1973.
Richard E. Quandt, ‘Probabilistic Errors in the Leontief System,’ Naval Research Logistics Quarterly, V, July, 1958.
Ibid., p. 159.
Wesley H. Long, ‘An Examination of Linear Homogeneity of Trade and Production Functions in County Leontief Matrices,’ Journal of Regional Science, IX, April, 1969, p. 47–69.
For a study which is similar to Long’s; but which uses less complete data, see Iwao Ozaki, ‘Economies of Scale and Input-Output Coefficients,’ Applications of Input-Output Analysis, ed. A. P. Carter and A. Brody, Amsterdam, North-Holland, 1970, p. 280-302.
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© 1976 H. E. Stenfert Kroese B. V., Leiden
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Gerking, S.D. (1976). Tests of the static, open input-output model: an appraisal. In: Estimation of stochastic input-output models. Studies in applied regional science, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-4362-2_2
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